Large aperture terahertz-gigahertz lens system

ABSTRACT

Lens systems used in a gigahertz/terahertz imaging system are proposed. Each proposed lens system may include two thin lens elements, spherical or aspherical, in which combined provides gigahertz-terahertz refractive power with a small f-number. The gigahertz-terahertz waves are diverted by the lens systems in such a way that it forms an image of an object, such as a human scale object, on a planar gigahertz-terahertz image sensor. The radius of curvatures, profile, sizes, spacing, and aspherical coefficients of the lens elements may be selected to achieve quality focusing performance. The spacing between the lens elements and the spacing between the lens elements and the image sensor may be adjusted to change both the focal length and the focusing distance to achieve optimum field of view and maximum imaging resolution. The size of the lens may be scaled with the size of the object or the lens aperture stop.

FIELD OF THE INVENTION

The present invention relates to a terahertz-gigahertz lens system that may be used to focus terahertz-gigahertz waves reflected off or transmitted through an object to an image sensor. In particular, the present invention describes a terahertz-gigahertz lens system with large aperture (small f-number) and high resolution power (only limited by diffraction) simultaneously, while keeping the overall size and weight reasonably contained.

BACKGROUND OF THE INVENTION

Terahertz-gigahertz imaging and sensing rely upon the effectiveness to control and divert the flow of the terahertz-gigahertz waves in free space. Although terahertz-gigahertz waves have been used as a security screening tool because of its unique transmission properties that identifies concealed objects, such as a metal weapon hidden under the fiber clothing, a single large aperture lens systems (that mitigates the diffraction limitation) with reduced aberration to achieve high image resolution while providing a field of view that covers a full human body (say 200 cm) is still on demand.

To make a terahertz-gigahertz camera that work in analogous to an optical camera that photographers uses, the camera lens is one essential part of the camera if not more important than the camera body itself. One of the serious problems with designing terahertz-gigahertz lenses is the material choice. The mainstream terahertz-gigahertz lenses are based on polymers (such as Topas, Roxolite, Polymethylpentene (TPX), Polyethylene (PE), or Teflon lenses) or dielectrics (such as silicon), which are not common optical materials that are used in standard large optical systems. This means that making large or aspherical gigahertz-terahertz lens elements (to further reduce weight) out of these materials may be expensive, impractical, or readily unavailable. In addition, polymers, albeit commonly used in making terahertz lenses, are in general less stable in harsh environmental conditions. Moreover, the refractive indices of these polymers are usually small, which means less refractive power and higher degree of design limitations.

The lens design in terahertz-gigahertz system is critical because important features found in optical cameras are currently lacking in terahertz-gigahertz cameras. These features include the ability to at least 1) achieve high resolution, and 2) have adjustable focal length through its lens design. For 1), the resolution in terahertz-gigahertz systems is intrinsically limited by the diffraction limitation of the lens. Therefore, it is desirable to make the diameter of the terahertz-gigahertz lens large, while at the same time to keep the lens as thin and light weight as possible. For 2), at least two lens elements are required to adjust the focal length of an optical system, which increases the design complexity, especially when the material absorption is factored in, but at the same time allows further improvement of the image quality. Using a lens system also has the advantage to reduce aberrations while maintaining the large aperture of the lens system, which is essential to provide both high resolution and flexible field of view for various imaging applications. However, the downside of using a lens system is the increased weight, absorption, cost, housing design, and design complexity. Therefore, limiting the number of lens elements and using thinner and lighter lens elements in the lens design is crucial.

Accordingly, there is a need to provide a terahertz-gigahertz lens system which has at least large aperture, high resolution, and adjustable focal length.

SUMMARY OF THE INVENTION

The present invention proposes the terahertz-gigahertz lens system with large aperture. The present invention achieves such terahertz-gigahertz lens system by using specific lenses configuration(s) with specific lens material(s).

The proposed lens systems for the terahertz-gigahertz waves provide a field-of-view that images human-scale object at a few meters away from the lens system, and simultaneously achieve large aperture size and high resolution. Focusing objects at different distances from the lens systems are enabled by changing the separation between the lens elements or by adjusting the position of the image sensor along the optical axis.

Some embodiments are several versions of lens system designs made of material(s) with specific refractive indices. In one embodiment, the lens elements are made of glass, and each lens element has two different spherical surfaces. In another embodiment, the lens elements are made of glass, and each of the two lens elements has one spherical surface and one aspheric surface. In yet another embodiment, the lens elements are made of quartz, one lens element has an aspherical surface and a spherical surface, and the other lens element has two different spherical surfaces. In one more embodiment, the lens elements are both made of quartz, where one lens element has a spherical surface and a planar surface, and the other lens element has two different spherical surfaces. Furthermore, for all the previous embodiments, the refractive index of material used to form the lens elements, the distance between the lens elements, the thickness of each lens element, and the radii of each lens surface may be altered slightly. Accordingly, the EFL (Effective Focal Length), the HFOV (Half Field-Of-View), and the F# (f-number) of each of the previous embodiments may be altered slightly and not limited strictly.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A to FIG. 1C are a cross-sectional illustration and two lens performance data of an embodiment of a terahertz-gigahertz lens system that includes two lens elements made of glass.

FIG. 2A to FIG. 2C are a cross-sectional illustration and two lens performance data of an embodiment of a terahertz-gigahertz lens system that includes two lens elements made of glass.

FIG. 3A to FIG. 3C are a cross-sectional illustration and two lens performance data of an embodiment of a terahertz-gigahertz lens system that includes two lens elements made of quartz.

FIG. 4A to FIG. 4C are a cross-sectional illustration and two lens performance data of an embodiment of a terahertz-gigahertz lens system that includes two lens elements made of quartz.

DETAILED DESCRIPTION OF THE INVENTION

Reference will now be made in details to specific embodiment of the present invention. Examples of these embodiments are illustrated in the accompanying drawings. While the invention will be described in conjunction with these specific embodiments, it will be understood that the intent is not to limit the invention to these embodiments. In fact, it is intended to cover alternatives, modifications, and equivalents as may be included within the spirit and scope of the invention as defined by the appended claims. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention. The present invention may be practiced without at least one of these specific details. In other instances, the well-known portions are less or not described in detail in order not to obscure the present invention.

Several embodiments of lens systems designed for terahertz-gigahertz waves are proposed. Various examples of the terahertz-gigahertz lens systems are proposed to resolve large objects at a reasonable distance. The proposed embodiments of lens systems may be implemented in or attached to any terahertz-gigahertz camera or imaging system (or sensing system) to provide the desired effective focal length.

Four of the present embodiments of the terahertz-gigahertz lens system are particularly illustrated. One illustrated embodiment has two lens elements made of glass that their surfaces are all spherical and different from each other, another illustrated embodiment has two lens elements made of glass that each has one spherical surface and one aspherical surface, the other illustrated embodiment has two lens elements made of quartz that one has two different spherical surface, and the other one has one spherical surface and one aspherical surface. One more illustrated embodiment has two lens elements made of quartz that one has a spherical surface and a planar surface, and the other one has two different spherical surfaces.

In addition, the illustration of the present embodiments are based on the assumption that the object is positioned on the left hand side of the lens systems and the image sensor is positioned on the right hand side of the lens system. Also, the illustrated lens elements are rotational symmetrical along the optical axis extending from the left hand side to the right hand side of the drawing.

Furthermore, each of illustrated embodiments has a specific effective focal length (EFL), a specific f-number and a specific half field-of-view (HFOV). That is to say, each of illustrated embodiments has a unique EFL, a unique f-number, and a unique HFOV. In other words, each variation of the present invention may have a unique EFL, a unique f-number and a unique HFOV. Note that the EFL may be adjusted through changing the distance between the two lens element, which also changes the HFOV and f-Number accordingly. The EFL is defined as the distance from the rear principal plane of lens system to the rear focal point positioned behind the last lens element (i.e., behind the rightmost surface of these lens elements) calculated at infinite conjugate. The HFOV is defined as: HFOV=tan⁻¹(SS/2f), where SS is the diameter (width or height if rectangular) of the image sensor, whereas the f-number (f) is defined as: f-number=EFL/D, where D is the diameter of the aperture stop. Of course, HFOV is a half of FOV (field-of-view), and both HFOV and FOV may be used to evaluate the performance of the lens system.

Optional, each proposed lens system may include an aperture stop located in front of the first lens element (i.e., in front of the leftmost surface of these lens elements). The aperture stop is used to block the un-desired terahertz-gigahertz waves, even other noise from entering the lens system. This aperture stop is designed to be located at or near the front vertex of the lens system, and is ideally centered with respect to the optical axis. The location of the aperture stop may be placed closer to or farther away from the first lens element to account for tolerances in lens assembly or other lens/system design constraints. Moreover, the dimension of the aperture stop may be adjusted to let in more light or less light, or to accommodate the physical limitations from the lens housing system that holds the lens system in place. The aperture stop may be made of materials such as metals, which reflects the gigahertz-terahertz waves, or absorbers, which absorbs gigahertz-terahertz waves, or even materials that made part of the lens housing system. Ideally, the aperture stop should also be covered by (or made of) terahertz-gigahertz absorptive materials to remove unwanted reflections. Reasonably, the diameter of the aperture stop reduces lens aberration but enhances diffraction of the proposed lens systems. For example, further closing the aperture stop will degrade the resolution power of the proposed lens systems if the lens system is already performing at the diffraction limit, whereas closing the aperture stop will improve the resolution power if the lens aberration dominates the image degradation (happens when terahertz-gigahertz waves are at higher frequencies).

Optional, each proposed lens system may include an image sensor located behind the second lens element (i.e., behind the rightmost surface of these lens elements). The image sensor is used to receive and detect the terahertz-gigahertz waves delivered through these lens elements. Any commercial, well-known, on-developed, or to-be-appeared sensor capable of receiving and detecting the terahertz-gigahertz waves may be used, the invention does not limit the details of the image sensor. For example, the image sensor may be achieved by using a 2D planar array of terahertz-gigahertz image sensors. Furthermore, the distance between the lens elements and the image sensor may be adjusted to allow focusing, for example, to form images of different objects (such as different object sizes) at different distances from the lens without modifying the configurations of the lens elements.

FIG. 1A illustrates the cross-sectional structure of an exemplary embodiment (lens system 100), which consists of two lens elements 101 and 102 positioned along the optical axis in sequence, where both are made of glass with refractive index 2.52 to cover the applications for terahertz-gigahertz waves within frequencies of 100 to 300 GHz. Both the left and the right surfaces of lens element 101 are spherical surfaces with different radii. Also, both the left and the right surfaces of lens element 102 are spherical surfaces with different radii. The lens system 100 may further include an aperture stop 120 and an image sensor 110. In lens system 100, the aperture stop 120 (surface 1) may be slightly misaligned from the left surface (surface 2) of the lens element 101, also the image sensor 110 is assumed to be a 10 cm×10 cm plane for the HFOV calculation. However, the sensor size is not strictly limited to this dimension because the lens illumination area (fixed) will only be smaller or larger than the adjusted sensor size.

The lens system data for lens system 100 shown in table 1A provides quality performance with an f-number of 0.92, an EFL of 267 mm, a HFOV of 11°, and a total track length (TTL) of 468 mm.

TABLE 1A Focal Length 267 mm Half Field-Of-View 11° f-number 0.92 Total track length 468 mm Design Frequency 100-300 GHz The lens system prescription for lens system 100 is shown in table 1B.

TABLE 1B Surface Thickness/ Refractive Element name # Radius Type Separation Material index Diameter Object Plane 0 INF FLAT 4500 mm 1.0 2000 mm Aperture Stop 120 1 INF FLAT   0 mm 1.0  290 mm Lens Element 101 (Left surface) 2  531 mm Spherical  27 mm Glass 2.52  300 mm Lens Element 101 (Right surface) 3 1636 mm Spherical  321 mm 1.0  300 mm Lens Element 102 (Left Surface) 4  188 mm Spherical  38 mm Glass 2.52  240 mm Lens Element 102 (Right Surface) 5  427 mm Spherical  52 mm 1.0  240 mm Image Plane 110 (Image Sensor) 6 INF FLAT NA NA  100 mm The radius is positive if the center of curvature is on the right hand side of the lens element. The diameter is the size on the cross-section perpendicular to the optical axis. The thickness/separation is defined as the distance between two adjacent neighboring surfaces along the optical axis. For example, the thickness/separation for surface 2 defines the thickness of lens element 101 along the optical axis, but the thickness/separation for surface 5 defines the distance between the right surface of lens element 102 to the image sensor 110 along the optical axis. The total track length TTL of a lens system is defined as the distance between the left surface of the leftmost lens element to the image sensor along the optical axis.

As shown on Table 1B, for both lens elements 101/102, the radius of the left surface (531 mm/188 mm) is smaller than the radius of the right surface (1636 mm/427 mm). The thickness (27 mm) of lens element 101 is smaller than the thickness (38 mm) of lens element 102, and the distance (0 mm) between the aperture stop 120 and lens elements 101 is smaller than the distance (52 mm) between lens elements 102 and image sensor 110. Such lens system 100 may be advantage to measure an object with a diameter 2000 mm positioned 4500 mm away the aperture stop 120 along the optic axis.

FIG. 1B and FIG. 1C are used to emphasize the performance of the example lens system 100. As shown on FIG. 1B, all of the calculated MTF (including both Tangential (T) and Sagittal (S)) vs Spatial Frequency curves at different object heights (T/S 0.00 mm, 707.00 mm and 1000.00 mm) appears to align well with the diffraction limited curve. As shown in FIG. 1C, whether the height of the object where the terahertz-gigahertz waves are coming from are 0 mm, 707 mm, or 1000 mm, the optical path difference are always below half of the wavelength on both the x-axis and the y-axis (while the optical axis being the z-axis). Note that the calculation here is based at 100 GHz.

FIG. 2A illustrates the cross-sectional structure of an exemplary embodiment (lens system 200), which consists of two lens elements 201 and 202 positioned along the optical axis in sequence, where both are made of glass with refractive index 2.52 to cover the applications for terahertz-gigahertz waves within a frequency range of 100 to 300 GHz. Both the left surfaces (surfaces 2 and 4) of lens element 201 and lens elements 202 are aspherical surfaces but different from each other. In contrast, both the right surfaces (surface 3 and 5) of lens element 101 and lens element 102 are spherical surfaces but different from each other. The example lens systems may further include an aperture stop 220 and an image sensor 210. In this example, the aperture stop 220 (surface 1) may be slightly misaligned from the left surface (surface 2) of the lens element 201, also the image sensor 210 is assumed to be a 10 cm×10 cm plane for the HFOV calculation. However, the sensor size is not strictly limited to this dimension as the lens illumination area (fixed) will only be smaller or larger than the adjusted sensor size.

The lens system data for lens system 200 shown in table 2A provides quality performance with an f-number of 0.70, an EFL of 211 mm, a HFOV of 13°, and a total track length (TTL) of about 302 mm.

TABLE 2A Focal Length 211 mm Half Field-Of-View 13° f-number 0.70 Total track length 302 mm Design Frequency 100-300 GHz

The lens system prescription for lens system 200 is shown in table 2B.

TABLE 2B Surface Thickness/ Refractive Element name # Radius Type Separation Material index Diameter Object Plane 0 INF FLAT 4500 mm 1.0 3000 mm Aperture Stop 220 1 INF FLAT   0 mm 1.0  300 mm Lens Element 201 (Left surface) 2 232 mm (vertex) Aspherical  45 mm Glass 2.52  320 mm Lens Element 201 (Right surface) 3 382 mm Spherical  181 mm 1.0  320 mm Lens Element 202 (Left Surface) 4 159 mm (vertex) Aspherical  32 mm Glass 2.52  170 mm Lens Element 202 (Right Surface) 5 172 mm Spherical  43 mm 1.0  170 mm Image Plane 210 (Image Sensor) 6 INF FLAT NA NA  100 mm In addition, the definitions of the radius, the diameter, the thickness/separation and the total track length TTL are equal to the above discussion. Further, the vertex of the lens surface referred here means the intersection point of the lens surface and the optical axis. If the surface type is aspherical, then the radius listed is defined as the radius of the curvature at the vertex of the lens surface.

As shown on Table 2B, for both lens elements 201/202, the radius of the left surface (232 mm/159 mm) is smaller than the radius of the right surface (382 mm/172 mm), and the thickness (45 mm) of lens element 201 is larger than the thickness (32 mm) of lens element 202. The distance (0 mm) between the aperture stop 220 and lens elements 201 is smaller than the distance (43 mm) between lens elements 202 and image sensor 210. Such lens system 200 may be advantage to measure an object with a diameter 2000 mm positioned 4500 mm away the aperture stop 220 along the optic axis.

FIG. 2B and FIG. 2C are used to emphasize the performance of the example lens system 200. As shown on FIG. 2B, all of the calculated MTF (including both Tangential (T) and Sagittal (S)) vs Spatial Frequency curves at different object heights (T/S 0.00 mm, 707.00 mm and 1000.00 mm) appears to align well with the diffraction limited curve. As shown in FIG. 2C, whether the height of the object where the terahertz-gigahertz waves are coming from are 0 mm, 707 mm, or 1000 mm, the optical path difference are always below half of the wavelength on both the x-axis and the y-axis (while the optical axis being the z-axis). Note that the calculation here is based at 100 GHz.

FIG. 3A illustrates the cross-sectional structure of an exemplary embodiment (lens system 300), which consists of two lens elements 301 and 302 positioned along the optical axis in sequence, where both lens elements 301 and 302 are made of quartz with a refractive index 1.96, to cover the applications for terahertz-gigahertz imaging within a frequency range of 300 to 500 GHz. For the lens element 301, the left surface (surface 2) is aspherical surface but the right surface (surface 3) is spherical surface. However, for lens element 302, both the left and the right surfaces (surfaces 4 and 5) are spherical surfaces and different from each other. The example lens systems 300 may further include an aperture stop 320 and an image sensor 310. In this example, the aperture stop 320 (surface 1) may be slightly misaligned from the left surface (surface 2) of the lens element 301, also the image sensor is assumed to be a 10 cm×10 cm plane for the HFOV calculation. However, the sensor size is not strictly limited to this dimension as the lens illumination area (fixed) will only be smaller or larger than the adjusted sensor size.

The lens system data for lens system 300 shown in table 3A provides quality performance with an f-number of 1.07, an EFL of 290 mm, a HFOV of 10°, and a total track length (TTL) of about 397 mm.

TABLE 3A Focal Length 290 mm Half Field-Of-View 10° f-number 1.07 Total track length 397 mm Design Frequency 300-500 GHz The lens system prescription for lens system 300 is shown in table 3B.

TABLE 3B Surface Thickness/ Refractive Element name # Radius Type Separation Material index Diameter Object Plane 0 INF FLAT 5500 mm 1.0 2000 mm Aperture Stop 320 1 INF FLAT   0 mm 1.0  270 mm Lens Element 301 (Left surface) 2 216 mm (vertex) Aspherical  50 mm Quartz 1.96  300 mm Lens Element 301 (Right surface) 3 1390 mm Spherical  284 mm 1.0  300 mm Lens Element 302 (Left Surface) 4 113 mm (vertex) Spherical  30 mm Quartz 1.96  150 mm Lens Element 302 (Right Surface) 5  163 mm Spherical  33 mm 1.0  150 mm Image Plane 310 (Image Sensor) 6 INF FLAT NA NA  100 mm In addition, the definitions of the radius, the diameter, the thickness/separation and the total track length TTL are equal to the above discussion. Further, the vertex of the lens surface referred here means the intersection point of the lens surface and the optical axis. If the surface type is aspherical, then the radius listed is defined as the radius of the curvature at the vertex of the lens surface.

As shown on Table 3B, for both lens elements 301/302, the radius of the left surface (216 mm/113 mm) is smaller than the radius of the right surface (1390 mm/163 mm), and the thickness (50 mm) of lens element 301 is larger than the thickness (30 mm) of lens element 302. The distance (0 mm) between the aperture stop 320 and lens elements 301 is smaller than the distance (43 mm) between lens elements 320 and image sensor 310. Such lens system 200 may be advantage to measure an object with a diameter 2000 mm positioned 5500 mm away the aperture stop 320 along the optic axis.

FIG. 3B and FIG. 3C are used to emphasize the performance of the example lens system 300. As shown on FIG. 3B, all of the calculated MTF (including both Tangential (T) and Sagittal (S)) vs Spatial Frequency curves at different object heights (T/S 0.00 mm, 707.00 mm and 1000.00 mm) appears to align well with the diffraction limited curve. As shown in FIG. 3C, whether the height of the object where the terahertz-gigahertz waves are coming from are 0 mm, 707 mm, or 1000 mm, the optical path difference are always below half of the wavelength on both the x-axis and the y-axis (while the optical axis being the z-axis). Note that the calculation here is based at 300 GHz.

FIG. 4A illustrates the cross-sectional structure of an exemplary embodiment (lens system 400), which consists of two lens elements 401 and 402 positioned along the optical axis in sequence, where both are made of quartz with refractive index 1.96 to cover the applications for terahertz-gigahertz waves within a frequency range of 100 to 300 GHz. For the lens element 401, the left surface (surface 2) is spherical surface but the right surface (surface 3) is a planar surface. However, for the lens element 402, both the left and the right surfaces (surfaces 4 and 5) are spherical surfaces but they are different from each other. The example lens systems 400 further includes an aperture stop 420 and an image sensor 410. In this example, the aperture stop 420 (surface 1) may be slightly misaligned from the left surface (surface 2) of the lens element 401, also the image sensor is assumed to be a 10 cm×10 cm plane for the HFOV calculation. However, the sensor size is not strictly limited to this dimension as the lens illumination area will only be smaller or larger than the adjusted sensor size.

The lens system data for lens system 400 shown in table 4A provides quality performance with an f-number of 0.71, an EFL of 200 mm, a HFOV of 14°, and a total track length (TTL) of about 339.4 mm.

TABLE 4A Focal Length 200 mm Half Field-Of-View 14° f-number 0.71 Total track length 339.4 mm Design Frequency 100-300 GHz The lens system prescription for lens system 400 is shown in table 4B.

TABLE 4B Surface Thickness/ Refractive Element name # Radius Type Separation Material index Diameter Object Plane 0 INF FLAT 4000 mm 1.0 2000 mm Aperture Stop 420 1 INF FLAT   0 mm 1.0  280 mm Lens Element 401 (Left surface) 2 334 mm Spherical  45 mm Quartz 1.96  300 mm Lens Element 401 (Right surface) 3 INF FLAT  205 mm 1.0  300 mm Lens Element 402 (Left Surface) 4 133 mm Spherical  40 mm Quartz 1.96  180 mm Lens Element 402 (Right Surface) 5 621 mm Spherical  49 mm 1.0  180 mm Image Plane 410 (Image Sensor) 6 INF FLAT NA NA  100 mm In addition, the definitions of the radius, the diameter, the thickness/separation and the total track length TTL are equal to the above discussion.

As shown on Table 4B, for both lens elements 401/402, the radius of the left surface (334 mm/163 mm) is smaller than the radius of the right surface (Infinite mm/623 mm), and the thickness (45 mm) of lens element 401 is smaller than the thickness (40 mm) of lens element 402. The distance (0 mm) between the aperture stop 420 and lens elements 401 is smaller than the distance (49 mm) between lens elements 402 and image sensor 410. Such lens system 400 may be advantage to measure an object with a diameter 2000 mm positioned 4000 mm away the aperture stop 420 along the optic axis.

FIG. 4B and FIG. 4C are used to emphasize the performance of the example lens system 400. As shown on FIG. 4B, all of the calculated MTF (including both Tangential (T) and Sagittal (S)) vs Spatial Frequency curves at different object heights (T/S 0.00 mm, 707.00 mm and 1000.00 mm) appears to align with the diffraction limited curve. As shown in FIG. 4C, whether the height of the object where the terahertz-gigahertz waves are coming from are 0 mm, 707 mm or 1000 mm, the optical path difference are always below half of the wavelength on both the x-axis and the y-axis (while the optical axis being the z-axis). Note that the calculation here is based at 100 GHz.

Moreover, the aspherical surface equations and coefficients for the aspherical surfaces illustrated above are all listed in Table 5.

TABLE 5 Surface K A B C Lens element 201 0  1.681439E−04 −3.294934E−09 0       (Left surface) Lens element 202 0  3.534696E−04  6.335390E−08 −1.084123E−11 (Left surface) Lens element 401 0 −5.017029E−04 −1.507751E−08 0       (Left surface) ${{Aspheric}\mspace{14mu} {Equation}\text{:}\mspace{14mu} {sag}} = {\frac{{cr}^{2}}{1 + \sqrt{1 - {\left( {1 + K} \right)c^{2}r^{2}}}} + {Ar}^{2} + {Br}^{4} + {Cr}^{6}}$ For the aspheric equation listed in Table 5, sag is the z-component of the displacement of the lens surface from the vertex, r is the r-component radial distance from the vertex, K is the conic constant, and c is the curvature at the vertex (equals to the reciprocal of the radius at the vertex listed in Tables). A, B, and C are the aspheric coefficients.

It should be emphasized that the parameters (including at least radius, thickness or distance, and refractive index) listed in lens prescriptions shown in tables 1B, 2B, 3B, and 4B may be altered slightly to achieve similar lens system performance, or to further reduce the lens aberrations, or to adapt with the corresponding lens housing design, or to account for the refractive index deviations in manufacturing, or to achieve other benefit(s). Of course, the variations of these dimensions automatically lead to changes of the corresponding parameters shown in Table 1A, 2A, 3A and 4A.

Table 6A and Table 6B present the design tolerance and the parameters' altered range, which present the acceptable variations of the example lens systems 100, 200, 300 and 400.

TABLE 6A Design Tolerance Distance between Design Refractive index Thickness Radius Lens Elements 100 ±0.2 ±10 mm ±10% 190-450 mm 200 ±0.2 ±10 mm ±10% 150-230 mm 300 ±0.2 ±10 mm ±10% 200-300 mm 400 ±0.16 ±10 mm ±10% 200-290 mm

TABLE 6B Parameter Range Design EFL HFOV Frequency F# 100 185-400 mm 7°-15° 80-300 GHz 0.64-1.38 200 195-241 mm 12°-14°  80-300 GHz 0.65-0.8  300 235-303 mm 9°-12° 80-500 GHz 0.87-1.12 400 197-281 mm  10°-14.2° 80-300 GHz 0.82-1.17 The geometrical configuration of the proposed lens systems are adjustable parameters, such as the thickness of the lens elements, the radius of each surface of the lens elements, and the distance between each pair of lens elements. Also, the material properties of the lens elements are only limited by their refractive indices. In other words, glass and quartz are only two example materials, but the lens elements may be made of any material whose refractive index is located in the range shown in Table 6A. Therefore, materials with similar refractive indices are acceptable variations to the example lens systems 100, 200, 300 and 400. To simplify the specifications and the drawings, the lens performance data of these acceptable variations are not particularly present.

Significantly, by referring to Table 6A and Table 6B, these exemplary embodiments illustrated in FIG. 1A, FIG. 2A, FIG. 3A and FIG. 4A may be slightly altered to generate other exemplary embodiments of this invention. For example, by referring to Table 6A and Table 6B, the variations of the lens system 100 illustrated in FIG. 1A may have lens element 101 with thickness about 17 to 37 mm (Table 1B presents 27 mm and Table 6A presents a range from subtracting 10 mm to adding 10 mm) and lens element 102 with thickness about 28 mm to 48 mm (Table 1B presents 38 mm and Table 6A presents a range from subtracting 10 mm to adding 10 mm), while the lens element 101 and lens element 102 may be separated at a distance about 190 to 450 mm (Table 6A directly presents such range). Surely, the radius of each surface of the two lens elements 101/102 may be amended by using the same way. For example, the variations of the lens system 100 illustrated in FIG. 1A may have lens element 101 whose left surface has radius about 477.1 mm to 584.1 mm (Table 1B presents 531 mm and Table 6A presents a range from subtracting 10% to adding 10%) and right surface has a radius about 1472.4 mm to 1799.6 mm (Table 1B presents 1636 mm and Table 6A presents a range from subtracting 10% to adding 10%), and also may have lens element 102 whose left surface has radius about 179.2 mm to 206.8 mm (Table 1B presents 188 mm and Table 6A presents a range from subtracting 10% to adding 10%) and right surface has a radius about 384.3 mm to 469.7 mm (Table 1B presents 427 mm and Table 6A presents a range from subtracting 10% to adding 10%). Furthermore, by referring to Table 6A, the variations of the lens system illustrated in FIG. 1A may have lens elements 101/102 made of material with refractive index from 2.32 to 2.72 (Table 1B presents refractive index 2.52 and Table 6A presents a range from subtracting 0.2 to adding 0.2), which increases the acceptable materials for forming the lens elements 101/102. Also, as shown in Table 6B, the variations of the lens system 100 illustrated in FIG. 1A may have EFL about 185 to 400 mm, HFOV about 7° to 15°, f-number about 0.64 to 1.38, and corresponding frequency about 80 to 300 GHz. Furthermore, for each lens system, for all materials with the acceptable refractive index, the material(s) with less weight and less absorption of terahertz-gigahertz waves at the corresponding frequency range shown in Table 6B are preferred. Clearly, for the variations of the lens system 100, an object positioned on the left side of the lens elements 101/102 and inside the FOV range 14° to 30° may be imaged by lens system 100. Of course, although not particularly presented herein, by referring to Table 6A and Table 6B, these exemplary embodiments illustrated in FIG. 2A, FIG. 3A, and FIG. 4A also may be slightly altered to generate other exemplary embodiments of this invention by the same approach as presented above for the exemplary embodiment illustrated in FIG. 1A.

In the exemplary embodiments, glass (or quartz) is used because it is easy to process to form the required profile of the lens elements, especially when the diameter of the lens elements is large and/or the lens element(s) has aspherical surface. In addition, the usage of quartz has an advantage that the electromagnetic loss of quartz is even lower. Note that the refractive index of quartz is usually less dependent on the frequency of the terahertz-gigahertz wave than the refractive index of the glass. Further, how the terahertz-gigahertz wave is absorbed in the material and how the refractive index is dependent on the frequency of the terahertz-gigahertz waves are two other factors to decide what material(s) and dimension(s) for the lens element(s) may be used.

Note that Table 6A allows adjustment of the distances between lens elements. That is to say, for this invention, the distance between lens elements not only may be fixed as shown in Tables 1B, 2B, 3B, and 4B, but also may be adjusted through the range shown in Table 6A, which leads to a flexible EFL/HFOV/f-number, which can be advantageous for many commercial and practical applications. In addition, although different examples discussed above may be suitable for forming an image of an object with diameter 2000 mm at different distances from 4000 mm to 5500 mm, the application of the present invention is not limited by this. Indeed, in the situation that the lens system is designed to form an image of an object with a diameter smaller than a maximum at about X mm and positioned on the left side of the first lens element with a separation about Y mm. The ratio of X to Y is a flexible variable and is dependent on the configuration of the lens system such as the materials of each lens element, the radii of each lens element, and the distance between different lens elements. Similarly, the distance between the image sensor and the right surface of the second lens element is also a variable, which is determined based on at least both the distance between the object and the lens system and the distance between the lens elements pairs.

Clearly, by using one or more examples (or variations) discussed above, an object with heights between about 80 cm to 200 cm in diameter (such as height and/or width) may form an image that covers the entire 100 cm² image sensor at a distance as close as about 0.5 meters to 5.5 meters away from the object, respectively. In such situation, the distance of the second lens element to the image sensor (image plane) may be adjusted to focus on the object. In addition, by using one or more lens system examples (or variations) discussed above, the lens system is capable of focusing objects of any size at a distance of 0.5 meters to infinity away from the lens system.

Furthermore, whether the material in use is glass and/or quartz, the gross weight of the lens system may be smaller than 10 kilograms.

Besides, although the examples discussed above possess an aperture stop which is positioned in front of the first lens elements and has both an infinite radius and a finite diameter about 300 mm, the invention does not limit the details of the aperture stop. For example, the aperture stop may have a diameter larger than 300 mm, even larger than the diameter of the first lens element. In such situation, it is reasonable to increase the diameter of the first element accordingly, but its edge thickness may become too thin and becomes impossible for manufacturing. In contrast, the aperture stop may have a diameter smaller than 300 mm, even smaller than the diameter of the first lens element (as listed on tables 1B/2B/3B/4B). In such situation, the diameter of the first lens element can be reduced to match the diameter of the aperture stop. In addition, in situations where the second lens element is positioned close to the image plane and the target object size becomes smaller, both the diameter of the second lens element and the image sensor may be reduced in proportional to the diameter of the object.

Variations of the methods, the devices, the systems and the applications as described above may be realized by one skilled in the art. Although the methods, the devices, the systems, and the applications have been described relative to specific embodiments thereof, the invention is not so limited. Many variations in the embodiments described and/or illustrated may be made by those skilled in the art. Accordingly, it will be understood that the present invention is not to be limited to the embodiments disclosed herein, can include practices other than specifically described, and is to be interpreted as broadly as allowed under the law. 

What is claimed is:
 1. A lens system has two lenses that form an image from the reflection or transmission of terahertz-gigahertz wave off an object.
 2. The lens system of claim 1, wherein each of the lenses is made of glass or quartz.
 3. The lens system of claim 1, wherein the object has a scale about from 80 cm to 200 cm in diameter and the object may be at a distance as close as about 0.5 meters to infinity from the lens system.
 4. The lens system of claim 1, wherein the image is detected by a two-dimensional planar terahertz-gigahertz image sensor with the size of about 10 cm².
 5. The lens system of claim 1, wherein the largest diameter of the lens elements is about 32 cm, and the f-number may be as low as 0.64.
 6. The lens system of claim 1, wherein the distance of the two lens elements may be adjusted to adjust the focal length of the lens system.
 7. The lens system of claim 1, wherein one or more of the lens surfaces is spherical.
 8. The lens system of claim 1, wherein one or more of the lens surfaces is aspherical.
 9. The lens system of claim 1, wherein the gross weight of the lens system is smaller than 10 kilogram.
 10. The lens system of claim 1, wherein the size of the lens elements may be scaled with the object size.
 11. A large aperture terahertz-gigahertz lens system, comprising: a first lens element, wherein the left surface of the first lens element is a spherical surface with a radius about 477.9 to 589.1 mm and a diameter about 300 mm, wherein the right surface of the first lens element is a spherical surface with a radius about 1472.4 to 1799.6 mm and a diameter about 300 mm, wherein the thickness of the first lens element is about 17 to 37 mm; and a second lens element, wherein the left surface of the second lens element is a spherical surface with a radius about 169.2 to 206.8 mm and a diameter about 240 mm, wherein the right surface of the second lens element is a spherical surface with a radius about 384.3 to 469.7 mm and a diameter about 240 mm, wherein the thickness of the second lens element is about 28 to 48 mm; wherein the distance between the first lens element and second lens element is about 190 to 450 mm; wherein the first lens element and the second lens element are positioned con-centered along an optical axis; wherein both the first lens element and the second lens elements are made of material(s) with refractive index about 2.32 to 2.72.
 12. The large aperture terahertz-gigahertz lens system as claimed in claim 11, wherein each of the lens elements is made of glass.
 13. The large aperture terahertz-gigahertz lens system as claimed in claim 11, further comprising an aperture stop positioned in front of the first lens element, the aperture stop has an infinite radius and a diameter about 290 mm, wherein the distance between the aperture stop and the left surface of the first lens element is about 0 mm.
 14. The large aperture terahertz-gigahertz lens system as claimed in claim 11, wherein the lens system has a HFOV range about 7° to 15°, wherein an object positioned on the left side of the lens elements and inside the FOV range about 14° to 30° may be sensed by an image sensor positioned on the right side of these lens elements.
 15. The large aperture terahertz-gigahertz lens system as claimed in claim 14, wherein the lens system is designed to form an image of an object with a diameter about 2000 mm and positioned on the left side of the first lens element with a separation about 4500 mm.
 16. The large aperture terahertz-gigahertz lens system as claimed in claim 11, further comprising an image senor positioned behind the second lens element, the image sensor has an infinite radius and a diameter about 100 mm, wherein the distance between the image sensor and the right surface of the second lens element is a variable based on both the distance between the object and the lens system and the distance between the two lens elements.
 17. The large aperture terahertz-gigahertz lens system as claimed in claim 11, further comprising an aperture stop positioned in front of the first lens elements, the aperture stop has an infinite radius and a finite diameter smaller than 300 mm, wherein the diameter of the first lens element may be reduced to match the diameter of the aperture stop.
 18. The large aperture terahertz-gigahertz lens system as claimed in claim 11, wherein the lens system is designed to form an image of an object positioned on the left side of the first lens element with a finite separation and has an image sensor positioned on the right side of the second lens element with a finite separation, wherein the diameter of the second lens element and the diameter of the image sensor may be reduced proportional to the diameter of the object.
 19. A large aperture terahertz-gigahertz lens system, comprising: a first lens element, wherein the left surface of the first lens element is an aspherical surface with a radius about 208.8 to 255.2 mm and a diameter about 320 mm, wherein the right surface of the first lens element is a spherical surface with a radius about 343.8 to 420.2 mm and a diameter about 320 mm, wherein the thickness of the first lens element is about 35 to 55 mm; and a second lens element, wherein the left surface of the second lens element is an aspherical surface with a radius about 143.1 to 174.9 mm and a diameter about 170 mm, wherein the right surface of the second lens element is a spherical surface with a radius about 154.8 to 189.2 mm and a diameter about 170 mm, wherein the thickness of the second lens element is about 22 to 42 mm; wherein the distance between the first lens element and second lens element is about 150 to 230 mm; wherein the first lens element and the second lens element are positioned con-centered along an optical axis; wherein both the first lens element and the second lens elements are made of material(s) with refractive index about 2.32 to 2.72.
 20. The large aperture terahertz-gigahertz lens system as claimed in claim 19, wherein each of the lens elements is made of glass.
 21. The large aperture terahertz-gigahertz lens system as claimed in claim 19, further comprising an aperture stop positioned in front of the first lens element, the aperture stop has an infinite radius and a diameter about 300 mm, wherein the distance between the aperture stop and the left surface of the first lens element is about 0 mm.
 22. The large aperture terahertz-gigahertz lens system as claimed in claim 19, wherein the lens system has a HFOV range about 12° to 14°, wherein an object positioned on the left side of the lens elements and inside the FOV range about 24° to 28° may be sensed by an image sensor positioned on the right side of these lens elements,
 23. The large aperture terahertz-gigahertz lens system as claimed in claim 22, wherein lens system is designed to form an image of an object with a diameter about 2000 mm and positioned on the left side of the first lens element with a separation about 4500 mm.
 24. The large aperture terahertz-gigahertz lens system as claimed in claim 19, further comprising an image senor positioned behind the second lens element, the image sensor has an infinite radius and a diameter about 100 mm, wherein the distance between the image sensor and the right surface of the second lens element is a variable based on both the distance between the object and the lens system and the distance between the two lens elements.
 25. The large aperture terahertz-gigahertz lens system as claimed in claim 19, further comprising an aperture stop positioned in front of the first lens elements, the aperture stop has an infinite radius and a finite diameter smaller than 300 mm, wherein the diameter of the first lens element may be reduced to match the diameter of the aperture stop.
 26. The large aperture terahertz-gigahertz lens system as claimed in claim 19, wherein the lens system is designed to form an image of an object positioned on the left side of the first lens element with a finite separation and has an image sensor positioned on the right side of the second lens element with a finite separation, wherein the diameter of the second lens element and the diameter of the image sensor may be reduced proportional to the diameter of the object.
 27. A large aperture terahertz-gigahertz lens system, comprising: a first lens element, wherein the left surface of the first lens element is an aspherical surface with a radius about 194.4 to 237.6 mm and a diameter about 300 mm, wherein the right surface of the first lens element is a spherical surface with a radius about 1251 to 1529 mm and a diameter about 300 mm, wherein the thickness of the first lens element is about 40 to 60 mm; and a second lens element, wherein the left surface of the second lens element is a spherical surface with a radius about 101.7 to 124.3 mm and a diameter about 150 mm, wherein the right surface of the second lens element is a spherical surface with a radius about 146.7 to 179.3 mm and a diameter about 150 mm, wherein the thickness of the second lens element is about 20 to 40 mm; wherein the distance between the first lens element and second lens element is about 200 to 300 mm; wherein the first lens element and the second lens element are positioned con-centered along an optical axis; wherein both the first lens element and the second lens elements are made of material(s) with refractive index about 1.76 to 2.16.
 28. The large aperture terahertz-gigahertz lens system as claimed in claim 27, wherein each of the lens elements is made of quartz.
 29. The large aperture terahertz-gigahertz lens system as claimed in claim 27, further comprising an aperture stop positioned in front of the first lens element, the aperture stop has an infinite radius and a diameter about 270 mm, wherein the distance between the aperture stop and the left surface of the first lens element is about 0 mm.
 30. The large aperture terahertz-gigahertz lens system as claimed in claim 27, wherein the lens system has a HFOV range about 9° to 12°, wherein an object positioned on the left side of the lens elements and inside the FOV range about 18° to 24° may be sensed by an image sensor positioned on the right side of these lens elements,
 31. The large aperture terahertz-gigahertz lens system as claimed in claim 30, wherein lens system is designed to form an image of an object with a diameter about 2000 mm and positioned on the left side of the first lens element with a separation about 5500 mm.
 32. The large aperture terahertz-gigahertz lens system as claimed in claim 27, further comprising an image senor positioned behind the second lens element, the image sensor has an infinite radius and a diameter about 150 mm, wherein the distance between the image sensor and the right surface of the second lens element is a variable based on both the distance between the object and the lens system and the distance between the two lens elements.
 33. The large aperture terahertz-gigahertz lens system as claimed in claim 27, further comprising an aperture stop positioned in front of the first lens elements, the aperture stop has an infinite radius and a finite diameter smaller than 300 mm, wherein the diameter of the first lens element may be reduced to match the diameter of the aperture stop.
 34. The large aperture terahertz-gigahertz lens system as claimed in claim 27, wherein the lens system is designed to form an image of an object positioned on the left side of the first lens element with a finite separation and has an image sensor positioned on the right side of the second lens element with a finite separation, wherein the diameter of the second lens element and the diameter of the image sensor may be reduced proportional to the diameter of the object.
 35. A large aperture terahertz-gigahertz lens system, comprising: a first lens element, wherein the left surface of the first lens element is an spherical surface with a radius about 300.6 to 367.4 mm and a diameter about 300 mm, wherein the right surface of the first lens element is a planar surface with an infinite radius and a diameter about 300 mm, wherein the thickness of the first lens element is about 35 to 55 mm; and a second lens element, wherein the left surface of the second lens element is a spherical surface with a radius about 119.7 to 146.3mm and a diameter about 180 mm, wherein the right surface of the second lens element is a spherical surface with a radius about 558.9 to 683.1 mm and a diameter about 180 mm, wherein the thickness of the second lens element is about 30 to 50 mm; wherein the distance between the first lens element and second lens element is about 200 to 290 mm; wherein the first lens element and the second lens element are positioned con-centered along an optical axis; wherein both the first lens element and the second lens elements are made of material(s) with refractive index about 1.80 to 2.12.
 36. The large aperture terahertz-gigahertz lens system as claimed in claim 35, wherein each of the lens elements is made of quartz.
 37. The large aperture terahertz-gigahertz lens system as claimed in claim 35, further comprising an aperture stop positioned in front of the first lens element, the aperture stop has an infinite radius and a diameter about 280 mm, wherein the distance between the aperture stop and the left surface of the first lens element is about 0 mm.
 38. The large aperture terahertz-gigahertz lens system as claimed in claim 35, wherein the lens system has a HFOV range about 10° to 14.2°, wherein an object positioned on the left side of the lens elements and inside the FOV range about 20° to 28.2° may be sensed by an image sensor positioned on the right side of these lens elements,
 39. The large aperture terahertz-gigahertz lens system as claimed in claim 38, wherein lens system is designed to form an image of an object with a diameter about 2000 mm and positioned on the left side of the first lens element with a separation about 4000 mm.
 40. The large aperture terahertz-gigahertz lens system as claimed in claim 35, further comprising an image senor positioned behind the second lens element, the image sensor has an infinite radius and a diameter about 100 mm, wherein the distance between the image sensor and the right surface of the second lens element is a variable based on both the distance between the object and the lens system and the distance between the two lens elements.
 41. The large aperture terahertz-gigahertz lens system as claimed in claim 35, further comprising an aperture stop positioned in front of the first lens elements, the aperture stop has an infinite radius and a finite diameter smaller than 300 mm, wherein the diameter of the first lens element may be reduced to match the diameter of the aperture stop.
 42. The large aperture terahertz-gigahertz lens system as claimed in claim 35, wherein the lens system is designed to form an image of an object positioned on the left side of the first lens element with a finite separation and has an image sensor positioned on the right side of the second lens element with a finite separation, wherein the diameter of the second lens element and the diameter of the image sensor may be reduced proportional to the diameter of the object. 